Modern Physics
Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 5, Problem 16P
To determine

The effect of circular disturbance created in the pond by using the terms of group and phase velocity.

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Find the phase velocity and group velocity for the following two wave-forms (x and t are measured in SI units) (i) 1(x,t) = cos(4t - 2x) + cos(8t- 4.r). (ii) 2(x,t) Does these waveforms satisfy the wave equation %3D = cos(8t- 6a) + cos (4t – 4.x). %3D v² Ət? where v is a constant independent of frequency. Explain.
The phase velocity v of gravity waves in a liquid of depth h is given by the formula v = tanh kh, k where g is the acceleration of free fall and k = 2w/2 is the wavenumber, a being the wavelength. Sketch the dispersion relation for such waves, and show that the group velocity is always between v2 and v. Find the phase and group velocities for gravity waves of frequency 1 Hz in a liquid of depth 0.1 m.
A free particle moving along positive x-axis encounter three regions as shown in the figure. The wave functions of the particle in region 1 and region 2 are of the form 4(x) = Asin(kx- wt). Where k=2T/A is a wave number and wt = o is the phase term. In region 1, the amplitude of the wave function A1=11.5, wavelength A1 = 4.97 nm and phase = -65.3°. The wavelength in region 2 is A2 = 10.5 nm. The boundary C is located at x = 0, and the boundary D is located at x = L, where L = 20 nm. Using the mathematical features of wave function, find the amplitude of the wave function and the phase in region 2. (A2 and ø2) Region 1 Region 2 Region 3 C D (x= 0) (x = L)
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